A131482 - OEIS

A131482

a(n) is the number of n-celled polyominoes with perimeter 2n+2.

1, 1, 2, 4, 11, 27, 83, 255, 847, 2829, 9734, 33724, 118245, 416816, 1478602, 5267171, 18840144, 67611472, 243378415, 878407170, 3178068821, 11523323634, 41865833602, 152382134767

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

2n+2 is the maximal perimeter of an n-celled polyomino. a(n) is the number of n-celled polyominoes that have a tree as their connectedness graph (vertices of this graph correspond to cells and two vertices are connected if the corresponding cells have a common edge).

LINKS

Table of n, a(n) for n=1..24.

Andrew Clarke, Isoperimetrical Polyominoes, The Poly Pages.

Herman Tulleken, Polyominoes 2.2: How they fit together, (2019).

FORMULA

a(n) <= A000105(n), a(n) <= A057730(n+1).

a(n) >= A000602(n) [see comment on edge graph trees]. - R. J. Mathar, Mar 08 2021

CROSSREFS

Cf. A000105, A057730. Diagonal of A342243.

A359522 counts only polyominoes with holes.

A002013 counts only unbranched polyominoes.

A038142 is the analog for polyhexes.